| Exam Board | WJEC |
|---|---|
| Module | Unit 1 (Unit 1) |
| Year | 2023 |
| Session | June |
| Marks | 6 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Binomial Theorem (positive integer n) |
| Type | Numerical approximation using expansion |
| Difficulty | Moderate -0.8 This is a straightforward application of the binomial theorem requiring only routine recall and substitution. Part (a) involves direct application of the binomial expansion formula with no algebraic complications, and part (b) is a standard 'hence' question with clear guidance on the substitution to use. The question requires minimal problem-solving and follows a common textbook pattern, making it easier than average. |
| Spec | 1.04a Binomial expansion: (a+b)^n for positive integer n |
| Answer | Marks |
|---|---|
| 1 | 0 |
| 1 | 1 |
| 1 | 2 |
| 1 | 3 |
| 1 | 4 |
Question 1:
1 | 0
1 | 1
1 | 2
1 | 3
1 | 4\begin{enumerate}[label=(\alph*)]
\item Using the binomial theorem, write down and simplify the first three terms in the expansion of $(1 - 3x)^9$ in ascending powers of $x$. [3]
\item Hence, by writing $x = 0.001$ in your expansion in part (a), find an approximate value for $(0.997)^9$. Show all your working and give your answer correct to three decimal places. [3]
\end{enumerate}
\hfill \mbox{\textit{WJEC Unit 1 2023 Q1 [6]}}